Welcome!Here's one direction you could go; I assume you're also playing with a 50-point max, in which case the Delta Flyer is just there to get more points onto Voyager. Both ships are designed to be fairly tanky, and Picard can get off a good Battlstations/Sacrificed transphasics strike that should devastate almost anything that isn't Borg.

I definitely felt like I was squandering points as I made this (Sacrifice? Really?), which is a sign that you'd benefit from another ship or two. The Tinyprise probably is indeed your best choice for both variety and power; Sulu and Cheat Death are still two of the Feds' best cards, Spock and Scotty synergize decently with Picard, and you can put Janeway on the ship itself.

Guessing from the setup it would probably first turn dock with Voyager and transfer Picard and Chekov (he is such a good combo with voyagers 360 aux). Use the Ent-D to drop antimatter mines on anything you do not like with Miles to disable something important.

As Evan said, use voyager to launch a huge transphasic hit to wreck something or at least leave it in a bad way next turn.

Given the 360 arcs your best bet is to blast past the romulan ships and make use of your 360 attack while behind them.

The Delta flyer can also make a very nice lifeboat for voyager, when things look to be about to go south jump picard and chekov back onto it and start shooting with whatever the delta flyer has left.

Guessing from the setup it would probably first turn dock with Voyager and transfer Picard and Chekov (he is such a good combo with voyagers 360 aux). Use the Ent-D to drop antimatter mines on anything you do not like with Miles to disable something important.

As Evan said, use voyager to launch a huge transphasic hit to wreck something or at least leave it in a bad way next turn.

Given the 360 arcs your best bet is to blast past the romulan ships and make use of your 360 attack while behind them.

The Delta flyer can also make a very nice lifeboat for voyager, when things look to be about to go south jump picard and chekov back onto it and start shooting with whatever the delta flyer has left.

This, exactly. In organized play, one would typically load up Voyager in the first round and then leave the shuttle there indefinitely; since such games often end with both players still having ships on the board, it's often easier to eke out a scoring advantage by taking the DF's 20 points out of the equation. (Come to think of it, maybe that build also wants Paris on the DF/Voyager instead of Enterprise)

That said, if you're doing an untimed fight to the death I suppose you might as well have the DF give its all. With that in mind, here's a slightly different version:

(Frankly I prefer Photonic Missiles, but that unused point was staring at me disapprovingly)What you'd do in this case is leave the weapon, hull plating, and Terrell on the DF so it can fend for itself and maybe give a nice little defensive buff to your capital ships. But to be honest I don't know much about shuttle combat, so grain of salt.